$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x + 5$ and $ BC = 6x + 6$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x + 5} = {6x + 6}$ Solve for $x$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({1}) + 5$ $ BC = 6({1}) + 6$ $ AB = 7 + 5$ $ BC = 6 + 6$ $ AB = 12$ $ BC = 12$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {12} + {12}$ $ AC = 24$